Quantification of the Steric Properties of 1,8-Naphthyridine-Based Ligands in Dinuclear Complexes

Steric properties of ligands are an important parameter for tuning the reactivity of the corresponding complexes. For various ligands used in mononuclear complexes, methods have been developed to quantify their steric bulk. In this work, we present an expansion of the buried volume and the G-parameter to quantify the steric properties of 1,8-napthyridine-based dinuclear complexes. Using this methodology, we explored the tunability of the steric properties associated with these ligands and complexes.


General considerations
Calculations were performed using ORCA software versions 4.0.1.2 (geometries of R (PNNP)Cu2Cl2 where R=Me, Ph, iPr, Cy and tBu) and 4.2.1. [1][2][3] The Becke 1988 exchange functional 4 was used in combination with the Perdew 1986 correlation functional (BP86) 5 . The redefinition of Ahlrichs triplezeta split valence basis set (def2-TZVP) was used on all atoms. 6 All calculations except those regarding the hydride dimerization were performed with Grimme's DFT-3 dispersion correction with Becke-Johnson damping. 7,8 Buried volume calculations were performed using the SambVca 2.1A web application following the methodology described below. 9 G-parameter calculations were performed using the Solid-G software using the methodology detailed below. 10 The starting geometries were obtained by modification of the closest available reported crystal structure. [11][12][13][14] Overlay tBu (PNNP)Cu 2 Cl 2 with reported crystal structure Figure S1: Overlay of the reported 12 crystallographically determined structure of tBu (PNNP)Cu2Cl2 (red) with the calculated structure (blue) showing a good match.

Buried volume calculations using the SambVca 2.1 A Web Application
For calculation of the total buried volume, the XYZ input file can be used directly as obtained from DFT calculations or single-crystal XRD analysis. Calculations requiring reproducible hemisphere analysis or orientation of the steric maps required manipulation of the input file, which was done using Chemcraft software 15 but this can be done with other software as well. To the structure of the molecule was added a dummy atom of arbitrary nature, and the angle between the dummy atom and both metal centers was set to 0 °. Next, the distance between the dummy atom and either metal atom was set to half the metal-metal distance. This structure was saved and used as input file for SambVca 2.1. In the SambVca 2.1 web application 9 , either the dummy atom, or both metal centers can be selected under the option "Select the atoms coordinated to the center of the sphere" and should give identical results. At "Select the atoms for z axis definition", the option "ADD DUMMY" was chosen, and subsequently the previously placed dummy atom, one of the metal centers and the carbon atom of the naphthyridine backbone closest to the midpoint (in between the nitrogen atoms) were selected. This adds a second dummy atom at 90 ° angles to the midpoint dummy atom (the first one to be selected) and the plane made up by the three selected atoms. For the option "Select the atoms for xz-plane definition" either of the metal centers can be selected. Under the option "Select the atoms to be deleted" both dummy atoms, all metal centers and coligands are selected and removed (co-ligands can also be removed beforehand, for example in Chemcraft). The sphere radius is the only other parameter that was changed in the SambVca S4 interface. To calculate the buried volume using the 'metal centric' approach, one of the metal centers was selected under the option "Select the atoms coordinated to the center of the sphere".
Step by step guide: 1. For the center of the sphere, select either both copper centers, or the dummy atom to be the center of the sphere. 2. In the next step, click 'add dummy' and select the midpoint dummy atom, one of the metal centers and the sp 2 carbon in between both nitrogen atoms (in that order). This will trigger the placement of a new (pink) dummy atom at 90° angles both to the first selected atom (the original dummy atom) and the plane defined by the three selected atoms. 3. For the definition of the xz-plane, select either of the metal centers. 4. Select all dummy atoms, co-ligands and metal centers and click 'delete selected atoms'. 5. The other options can be ignored, except for the sphere radius, which can be set according to preference (in this case, 5 Å). 6. After submitting the calculation, the steric parameters and steric map are provided in the proper orientation for hemisphere analysis. In this case, the reaction hemisphere is defined by the SW and SE quadrants, and the backbone hemisphere by the NW and NE quadrants. For other orientations, other axes can be defined in step 2 and 3.

Solid angle calculations using Solid-G
For the solid angle/G-parameter calculations, again a dummy atom was added at the midpoint between both metal centers. The other metal centers and co-ligands were removed beforehand (not strictly necessary). For the metal centered calculations, input files with only one of the metal centers present were made. The Solid-G program 10 requires a specific input file with all atoms numbered uniquely. This requires manipulation of the XYZ file beforehand, which can be done manually or more easily by numbering each atom uniquely in Microsoft Excel. In Solid-G the appropriate center of the sphere was chosen in the first step, and the other steps were done with standard settings.
Step by step guide: 1. Open the file with the XYZ coordinates in the Solid-G program. Make sure the atoms are labelled individually (C1, C2, C3 etc.). If the program you are using to generate the XYZ file does not have this as a standard option, use a text editor to change the XYZ file. Additionally, the file with the dummy atom as explained before is used, where the original metal centers and co-ligands are removed. 2. Type the label of the dummy atom "Bi1" and click 'Select Atom' to make the atom the center of the sphere.      Influence of the Cu-Cu and P-P distance on the steric parameters

Influence of M-M distance on other ligands
In order to assess the influence of the M-M distance on the steric parameters for other 1,8naphthyridine ligands, we investigated the steric properties of three cobalt complexes reported by Uyeda and co-workers. 16 The reported solid state structures were used for the calculations of the buried volume and G-value (table S4). An important difference between the NDI and the PNNP system is the flexibility. In the PNNP system, a change in M-M distance also caused a similar change in P-P distance. In the NDI system, however, the ligand twists upon increasing M-M distance and the N-N distance hardly changes. The M-M distance in this case therefore also does not correlate with the steric parameters in the way it did for the PNNP system. Dependence of the first coordination sphere size on metal-metal distance In the buried volume calculations, the sphere with a radius of 5 Å centered at the midpoint between the two metal centers serves as a reasonable first coordination sphere. Given the large dependence of the steric environment on metal-metal distance, we reasoned that, changing this sphere size depending on the metal-metal distance seemed intuitive.
When again looking at Figure 3, the Vbur (%) does not have a large dependence on the sphere radius, as long as this radius is between 3.5 and 5.5 Å. Typical metal-metal distances in the expanded pincer ligand are roughly between 2 and 3 Å. When one considers a sphere that encompasses both 3.5 Å spheres on the metal atoms (Figure 2), this difference of 1 Å would lead to a change in sphere radius of 0.5 Å leading to only minimal differences in Vbur (%). Sphere radii adjusted in this way were used to calculate the buried volume for three tBu (PNNP) dicopper complexes with Cu-Cu distances between 2.5 and 3.0 Å (Table S4). Indeed, the adjusted buried volumes are only marginally different S12 from the original buried volumes. The overall trend in buried volume depending on the sphere radius is also similar for these complexes, as shown in Figure S4. This confirms that the effect of this type of adjustment of the sphere radius is indeed minimal and hence the choice for a 5 Å sphere seems robust.

Different symmetries in PNNP complexes
To examine to which extend the twists and tilts of PNNP complexes impact the steric encumbrance, the optimized geometry of some of the R (PNNP)Cu2Cl2 complexes with R = Ph, Cy and C6F5 was taken (figure S6), and the R groups were changed to tert-butyl groups while leaving the rest of the molecular coordinates fixed. The geometry of only the R groups was then optimized while the rest of the geometry was frozen. The results of these calculations (table S5) provide an indication of the effect of these geometrical changes on the steric encumbrance.

Methylated ligand
For the complex with methyl substituted phosphines, the methylated structure features a tilted naphthyridine plane as opposed to the C2V symmetric non-methylated structure ( Figure S7). This causes the copper atoms to be below the naphthyridine plane, but above the P-P line, which creates in effect a similar situation as with the other structures. In this case, the copper atoms are pulled toward each other by the bridging chlorides and the naphthyridine N-atoms on one hand, while being pulled apart by the phosphines that are now not in line with the copper atoms due to the induced tilt. This then leads to a net elongation of the Cu-Cu distance with respect to the nonmethylated structure. For the H substituted analogue, this effect is not present since the methyl groups are too far from the Hs on the phosphines to effect such a change.

Hydride dimerization equilibrium
For calculating the dimerization energies for R (PNNP*)Cu2H (scheme 3 and figure 11) the geometries of the monomer and the dimer were optimized (BP86/def2-TZVP) and the Gibbs free energy of dimerization was calculated. Then the geometry of the monomer was used to calculate the steric parameters (i.e. Vbur and G, Table S7) as described before.
The dimerization energies are calculated without dispersion correction in the DFT method. Dispersion correction, in the case of the [ R (PNNP*)Cu2H]2 dimers, overestimates the dispersion energy and hence also the dimerization energy. This is evident when comparing the crystal structure of [ tBu (PNNP*)Cu2H]2 with the optimized structure with and without dispersion correction as was reported before. 12 Using a method without dispersion correction does yield a structure that corresponds well to the crystal structure, however, a positive dimerization energy is calculated for the [ tBu (PNNP*)Cu2H]2 complex (i.e. dimerization costs energy). This is contradictory to the experimental observations that show that this complex is a dimer both in solution and in solid state. 12 The dimerization energy that is calculated without dispersion correction is offset by the true dispersive energy (that is by definition attractive), which is why the calculated dimerization energies are higher than they are in reality. Given that the calculated structure without dispersion correction more closely resembles the experimentally determined structure than the one calculated with dispersion correction, we infer that the error introduced by the dispersion correction is larger than the one created by leaving this correction out, also in the case of the dimerization energies. As a potential alternative, we considered using the geometries of calculated structures without dispersion correction, and perform a single point calculation with dispersion correction. This does lead to a negative dimerization energy (-41.8 kcal/mol) for the tBu structure, however, reasoning along the same lines as above, we suspect that the error introduced by the dispersion correction is still quantitatively larger than the one introduced without it.
Additionally, Basisset Superposition Error (BSSE) was investigated as a potential cause for the overestimation of the dimerization energy. To get an estimate for the magnitude of this BSSE, a counterpoise correction was used as described in the Orca 4.2.1 manual (8.1.6) 20 for the tBu (PNNP)*Cu2H structures calculated without dispersion correction. This yielded a BSSE of 3.6 kcal/mol, indicating that this error is likely too small to account for the discrepancy we found between the experiment and the calculated value. In addition, we performed a geometry optimization with a geometrical Counterpoise Correction (gCP) as described in the Orca 4.2.1 manual (9.3.2.13) 20 and GD3BJ dispersion correction, and this yielded a similarly distorted structure as was found without the counterpoise correction ( Figure S15). From this we conclude that the BSSE is not the main cause for the observed error in the calculated dimerization energy. Figure S18: Overlay of the reported 12  For the isopropyl R (PNNP*)Cu2H complexes, three different conformations of the monomer and three of the dimer were calculated. For calculating the sterics parameters, the three monomer structures were used, leading to three values for each parameter. These three were then averaged and this average was plotted. The error bars shown in figure 11 show the largest deviation of one of the single values from the average since it is to indicate an order of magnitude of the error introduced by these different conformations. For calculating the dimerization energies, first the dimerization energy of the three pairs of different conformers was calculated. Then, these were averaged and that average was plotted. To obtain the error bars, the largest deviation from the average of one of the three dimerization energies was taken and this was plotted as the error. The analogous method was applied for the ethyl substituents, but in this case with two different conformations.  Figure S19: Different conformations of the Et groups on Et (PNNP*)Cu2H complexes used to calculate their dimerization equilibrium. Figure S20: Different conformations of the iPr groups on iPr (PNNP*)Cu2H complexes used to calculate their dimerization equilibrium.